The two incidents happened in the Tumene Dr and Westminster Dr area, in Owhata.
Rotorua police Inspector Ed Van Den Broek said no arrests had been made and police were tasking more patrols in the area.
However, Mr Van Den Broek said it was important members of the public were aware of this type of activity.
He said any suspicious activity should be reported to police by calling 111.
"Perhaps the most important way parents can protect their children is to teach them to be wary of potentially dangerous situations," he said.
"Help children recognise the warning signs of suspicious behaviour. Such as when an adult asks them to disobey their parents or do something without permission, asks them to keep a secret, asks children for help, or makes them feel uncomfortable in any way."
He said it was also important to teach children they could say no to an adult.
"You should also talk to your children about how they should handle dangerous situations. One way is to teach them - no, go, yell, tell.
"If in a dangerous situation kids should say no, run away, yell as loud as they can and tell a trusted adult what happened right away."
Mokoia Intermediate principal Deborah Epp agreed with Mr Van Den Broek and said children approached by strangers should say no, run away and tell an adult.
She said if the stranger harassed, pursued or touched them, they should also start yelling.
Mrs Epp, who is also the Rotorua Principals' Association president, said the Year 8 child from Mokoia Intermediate who was approached last week had done the right thing.
She said as part of their health programme at Mokoia Intermediate they taught their pupils about stranger danger.
Mrs Epp said she understood most other schools in Rotorua also taught their students about stranger danger.
